Paradoxes and inconsistent mathematics:
Logical paradoxes - like the Liar, Russell's, and the Sorites - are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber u...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2021
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| Schlagworte: | |
| Online-Zugang: | DE-12 DE-473 DE-706 URL des Erstveröffentlichers |
| Zusammenfassung: | Logical paradoxes - like the Liar, Russell's, and the Sorites - are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses "dialetheic paraconsistency" - a formal framework where some contradictions can be true without absurdity - as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 11 Oct 2021) Introduction to an inconsistent world -- Paradoxes; or, "Here in the presence of an absurdity" -- In search of a uniform solution -- Metatheory and naive theory -- Prolegomena to any future inconsistent mathematics -- Set theory -- Arithmetic -- Algebra -- Real analysis -- Topology -- Ordinary paradox |
| Beschreibung: | 1 Online-Ressource (xii, 324 Seiten) |
| ISBN: | 9781108993135 |
| DOI: | 10.1017/9781108993135 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:49:57Z |
| indexdate | 2024-07-20T04:45:52Z |
| institution | BVB |
| isbn | 9781108993135 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033035099 |
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| publishDate | 2021 |
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| publisher | Cambridge University Press |
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| spelling | Weber, Zach ca. 20./21. Jh. (DE-588)1248175271 aut Paradoxes and inconsistent mathematics Zach Weber Cambridge Cambridge University Press 2021 1 Online-Ressource (xii, 324 Seiten) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 11 Oct 2021) Introduction to an inconsistent world -- Paradoxes; or, "Here in the presence of an absurdity" -- In search of a uniform solution -- Metatheory and naive theory -- Prolegomena to any future inconsistent mathematics -- Set theory -- Arithmetic -- Algebra -- Real analysis -- Topology -- Ordinary paradox Logical paradoxes - like the Liar, Russell's, and the Sorites - are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses "dialetheic paraconsistency" - a formal framework where some contradictions can be true without absurdity - as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary Logic, Symbolic and mathematical Inconsistency (Logic) Dialetheism Paradox Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Paradoxon (DE-588)4044593-8 gnd rswk-swf Inkonsistenz (DE-588)4226191-0 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s Inkonsistenz (DE-588)4226191-0 s DE-604 Paradoxon (DE-588)4044593-8 s Erscheint auch als Druck-Ausgabe 978-1-108-83441-4 https://doi.org/10.1017/9781108993135 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Weber, Zach ca. 20./21. Jh Paradoxes and inconsistent mathematics Logic, Symbolic and mathematical Inconsistency (Logic) Dialetheism Paradox Mathematische Logik (DE-588)4037951-6 gnd Paradoxon (DE-588)4044593-8 gnd Inkonsistenz (DE-588)4226191-0 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4044593-8 (DE-588)4226191-0 |
| title | Paradoxes and inconsistent mathematics |
| title_auth | Paradoxes and inconsistent mathematics |
| title_exact_search | Paradoxes and inconsistent mathematics |
| title_exact_search_txtP | Paradoxes and inconsistent mathematics |
| title_full | Paradoxes and inconsistent mathematics Zach Weber |
| title_fullStr | Paradoxes and inconsistent mathematics Zach Weber |
| title_full_unstemmed | Paradoxes and inconsistent mathematics Zach Weber |
| title_short | Paradoxes and inconsistent mathematics |
| title_sort | paradoxes and inconsistent mathematics |
| topic | Logic, Symbolic and mathematical Inconsistency (Logic) Dialetheism Paradox Mathematische Logik (DE-588)4037951-6 gnd Paradoxon (DE-588)4044593-8 gnd Inkonsistenz (DE-588)4226191-0 gnd |
| topic_facet | Logic, Symbolic and mathematical Inconsistency (Logic) Dialetheism Paradox Mathematische Logik Paradoxon Inkonsistenz |
| url | https://doi.org/10.1017/9781108993135 |
| work_keys_str_mv | AT weberzach paradoxesandinconsistentmathematics |